Subgroups — C₃×C₇⋊#13091733 #44501400

Order 30660.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×D₃₆₅	C₂	1	1	yes	maximal, characteristic
2	C₇⋊#13091733	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅×C₇×C₇₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₇⋊#64408	—	5	1	no	maximal, Hall
5	C₇×D₃₆₅	C₂×C₃	1	1	yes	characteristic
6	C₃×#13091733	—	7	1	no	maximal, Hall
7	C₃×C₇×D₇₃	—	5	1	no	—
8	C₅×C₇×C₇₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
9	C₃×D₃₆₅	D₇	1	1	yes	characteristic
10	C₇⋊#64408	—	5	1	no	Hall
11	C₃×C₇×C₇₃	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
12	#13091733	—	7	1	no	Hall
13	C₃×C₅×C₇₃	Dic₇	1	1	yes	characteristic, complemented, Hall
14	C₇×D₇₃	—	5	1	no	—
15	C₃×#64408	—	35	1	no	Hall
16	D₃₆₅	C₃×D₇	1	1	yes	characteristic
17	C₇×C₇₃	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
18	C₃×D₇₃	—	5	1	no	—
19	C₃×C₇⋊AGL(1,𝔽₅)	—	73	1	no	maximal, Hall
20	C₅×C₇₃	C₃×Dic₇	1	1	yes	characteristic, complemented, Hall
21	#64408	—	35	1	no	Hall
22	C₃×C₇₃	C₇⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
23	C₃×C₇×D₅	—	73	1	no	—
24	D₇₃	—	5	1	no	—
25	C₇⋊AGL(1,𝔽₅)	—	73	1	no	Hall
26	C₃×C₅×C₇	#64408	1	1	yes	characteristic, complemented, Hall
27	C₃×Dic₇	—	365	1	no	Hall
28	C₇₃	C₃×C₇⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
29	C₇×D₅	—	73	1	no	—
30	C₃×AGL(1,𝔽₅)	—	511	1	no	Hall
31	C₂×C₃×C₇	—	365	1	no	—
32	C₅×C₇	C₃×#64408	1	1	yes	characteristic, complemented, Hall
33	C₃×D₅	—	73	1	no	—
34	Dic₇	—	365	1	no	Hall
35	C₃×C₇	#13091733	1	1	yes	characteristic, complemented, Hall
36	AGL(1,𝔽₅)	—	511	1	no	Hall
37	C₃×C₅	C₇⋊#64408	1	1	yes	characteristic, complemented, Hall
38	C₂×C₇	—	365	1	no	—
39	C₃×C₄	—	2555	1	no	Hall
40	D₅	—	73	1	no	—
41	C₇	C₃×#13091733	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₃	—	365	1	no	—
43	C₅	C₃×C₇⋊#64408	1	1	yes	characteristic, complemented, Sylow
44	C₄	—	2555	1	no	Sylow
45	C₃	C₇⋊#13091733	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	—	365	1	no	—

	subgroup	G/H
center, hypercenter	C₃	C₇⋊#13091733
commutator, hypocenter	C₅×C₇×C₇₃	C₃×C₄
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₇₃	C₄
prime radical	C₃×C₇×D₃₆₅	C₂
cosocle	C₇×D₃₆₅	C₂×C₃
LCS	G ▷ C₅×C₇×C₇₃
UCS	C₁ ◁ C₃

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₇⋊#13091733	C₃	direct (N × H)
3. C₃×C₅×C₇×C₇₃	C₄	semidirect
8. C₅×C₇×C₇₃	C₃×C₄	semidirect
11. C₃×C₇×C₇₃	AGL(1,𝔽₅)	semidirect
13. C₃×C₅×C₇₃	Dic₇	semidirect
17. C₇×C₇₃	C₃×AGL(1,𝔽₅)	semidirect
20. C₅×C₇₃	C₃×Dic₇	semidirect
22. C₃×C₇₃	C₇⋊AGL(1,𝔽₅)	semidirect
26. C₃×C₅×C₇	#64408	semidirect
28. C₇₃	C₃×C₇⋊AGL(1,𝔽₅)	semidirect
32. C₅×C₇	C₃×#64408	semidirect
35. C₃×C₇	#13091733	semidirect
37. C₃×C₅	C₇⋊#64408	semidirect
41. C₇	C₃×#13091733	semidirect
43. C₅	C₃×C₇⋊#64408	semidirect
45. C₃	C₇⋊#13091733	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₇×D₃₆₅	2
C₇⋊#13091733	3
C₃×C₇⋊#64408	5
C₃×#13091733	7
C₃×C₇⋊AGL(1,𝔽₅)	73

Subgroups — C3×C7⋊#13091733 #44501400

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇⋊#13091733 #44501400